The number of traders is increasing more than before as more people are generally becoming more interested in ways to become more financially independent and as thus in search of skills like trading.
Does the number of traders directly affect the volatility of the market? If it does, can we assume that trading was easier before with less traders (less volatility) than now when there are more traders, and the market more volatile?
Yes, when there will be more traders, then there will be more money in the market. which means more traders won't have the same sentiments (if they have then that's a good thing) but if they don't like some have bullish and some have bearish sentiments then predicting the market becomes a little difficult. But if the greed index is overall showing a greed score high then that's mean overall market's users are bullish and trading won't be that difficult in that timezone.
Just like it is now, if you see the greed index at high score on CMC, market is bullish, but if the sentiments of some of the users changes and if those users have high volumes then market's volatility will also changes. In my opinion, if more traders are joining but they have less money then that's not matter at all. All that matters to market's volatility is high volume of money flowing in and out. I hope you got my point.